Answer:
Graphic Representation of the Equations is in the image above
Step-by-step explanation:
Solve by Substitution :
// Solve equation [2] for the variable y
[2] y = 4x - 5
// Plug this in for variable y in equation [1]
[1] (4x-5) - 2x = -1
[1] 2x = 4
// Solve equation [1] for the variable x
[1] 2x = 4
[1] x = 2
// By now we know this much :
y = 4x-5
x = 2
// Use the x value to solve for y
y = 4(2)-5 = 3
Solution :
{y,x} = {3,2}
Answer:
See picture attached.
Step-by-step explanation:
Start with the y-intercept of -2 and plot that on the graph. Then, use the slope of 1/2x to plot more points to help you draw the line. Remember rise over run. Go up one from the y-intercept and right two. If you need to, you can also go down one and left two.
Hope this makes sense.
Answer:
y= -2x -8
Step-by-step explanation:
I will be writing the equation of the perpendicular bisector in the slope-intercept form which is y=mx +c, where m is the gradient and c is the y-intercept.
A perpendicular bisector is a line that cuts through the other line perpendicularly (at 90°) and into 2 equal parts (and thus passes through the midpoint of the line).
Let's find the gradient of the given line.
Gradient of given line
The product of the gradients of 2 perpendicular lines is -1.
(½)(gradient of perpendicular bisector)= -1
Gradient of perpendicular bisector
= -1 ÷(½)
= -1(2)
= -2
Substitute m= -2 into the equation:
y= -2x +c
To find the value of c, we need to substitute a pair of coordinates that the line passes through into the equation. Since the perpendicular bisector passes through the midpoint of the given line, let's find the coordinates of the midpoint.
Midpoint of given line
Substituting (-3, -2) into the equation:
-2= -2(-3) +c
-2= 6 +c
c= -2 -6 <em>(</em><em>-</em><em>6</em><em> </em><em>on both</em><em> </em><em>sides</em><em>)</em>
c= -8
Thus, the equation of the perpendicular bisector is y= -2x -8.